Pauli Exclusion Principle
The Pauli exclusion principle is the quantum mechanical principle that says that two identical fermions (particles with half-integer spin) cannot occupy the same quantum state simultaneously. In the case of electrons, it can be stated as follows: it is impossible for two electrons of a poly-electron atom to have the same values of the four quantum numbers (n'', ''ℓ, mℓ and ms). For two electrons residing in the sameorbital, n'', ''ℓ, and mℓ are the same, so ms must be different and the electrons have opposite spins. This principle was formulated by Austrian physicist Wolfgang Pauli in 1925. Tossup Questions # The term raised to the negative twelfth power in the Lennard-Jones potential accounts for this rule. White dwarfs exhibit electron degeneracy pressure, a factor limiting how much they can compress based on this rule. In general, this rule applies to half-spin particles called fermions meaning two particles can occupy the same region if and only if they have opposing (*) spins. For 10 points, name this rule of quantum mechanics typically stated as no two electrons can have the same four quantum numbers. # In the liquid drop model, this idea is responsible for the asymmetry energy. This rule is the reason that, at absolute zero, Fermi gases has greater energy ideal gases. Because its nuclei obey this rule, helium-3 has two superfluid phases rather than one. The Hartree-Fock method includes this statement implicitly by assuming the wavefunction is a Slater determinant. This law is a consequence of having a system with a wavefunction that is antisymmetric with respect to interchanging coordinates. It is responsible for the degeneracy pressure seen in white dwarfs and neutron stars. For 10 points, name this requirement that Fermions in the same location must have different quantum numbers, a principle most often applied to the electrons in an atom. # The EPR paradox requires that either this principle or locality must be broken. One of the consequences of this principle is the existence of the Tolman-Oppenheimer-Volkoff limit of neutron stars, because it provides for the degeneracy pressure that supports them. Although (*) bosons do not obey it, this law applies for all particles governed by Fermi-Dirac statistics. For 10 points, what principle, which states that no two fermions can share all four quantum numbers, forces electrons in the same subshell to have different spin? # It calls for an even number of protons and neutrons according to the liquid drop model, and it is also expressed in the Wiezsaecker formula, and it described the necessity for a colour quantum number for the quarks. Another important conclusion of it is the formation of the "Fermi-level" when a metal is cooled to absolute zero. This statement also describes why the degeneracy pressure helps white dwarves survive, and it was first posited to explain some anomalous spectroscopic results observed in the Zeeman effect. For 10 points, identify this statement which states that no two Fermions can possess the same set of quantum numbers. # Slater determinants are used to ensure a system obeys this principle, and Oscar Greenberg proposed the concept of color to account for it. White dwarfs are prevented from collapsing into black holes by electron degeneracy pressure, a consequence of this principle. It only applies to particles with antisymmetric wave functions, and thus, (*) bosons are not governed by this principle, while fermions are. For 10 points, name this principle that results in no two electrons being able to occupy identical quantum states.